## Description

For blocks only, vertex-centered volume measures the volume of the control volume in the dual
mesh centered around each grid point (i.e. volume cell vertex) in the block. This metric is
computed by subdividing each volume cell into sectors using the cell's vertices, edge midpoints,
face centroids, and volume centroid. The diagram below shows how one such sector is defined
around one of the vertices of a hexahedral volume cell.

The diagram shows the sector (shown in red) of a volume cell (outlined in gray) that contributes to the dual control
volume around a vertex (denoted by a black circle). The sector is defined by connecting the
vertex, 3 edge midpoints (denoted by blue circles), 3 face centroids (denoted by green squares),
and the volume centroid (denoted by a yellow triangle) to form a hexahedral element.

**Tip:** Use the probe
functionality while in the *Examine* command to visualize the dual mesh
control volume when examining any vertex-centered function.

This subdivision results in one
hexahedral sector (shown in red) for each vertex in the volume cell regardless of volume cell
type. The volume of the vertex's control volume is then computed by summing together the
volume of each of its contributing sectors.

**Note:** A pyramid can be thought of as a hexahedron with one
collapsed face. In the example diagram above, if you collapse the front face of the
hexahedral volume cell, the corresponding face of the sector (shown in red) also
collapses. The apex vertex of pyramids is associated with four collapsed hexahedron
sectors, one from each vertex in the volume cell that collapsed to form the apex.

For this function, the probe renders the vertex and the bounding faces of the dual mesh control
volume. Be aware that this metric may vary from the volume reported by
your vertex-centered solver due to the fact that there are several different methods for defining the dual
mesh.